Planck Sphere Cosmology: The Minimal Unit of the Universe and Its Unified Description of Fundamental Physics

This paper proposes the Planck Sphere — a sphere of radius equal to the Planck length ℓP — as the minimal geometric unit of the universe. Starting from the core identity: A_P × c³ = 4π × ℏ × G we demonstrate that the fundamental constants of nature (c, G, ℏ) are mutually determined through the Planck Sphere's surface area AP and the geometric factor 4π. From this single relation, we derive the Planck length, time, energy, mass, and temperature, as well as the information content of the Planck Sphere (I = π bits). Extended equivalences incorporating electromagnetic (ε₀, qP) and thermal (kB, TP) quantities are shown to follow naturally. We further propose that the cosmological constant Λ is not a true constant but varies as Λ(t) ~ 1/R(t)², consistent with recent DESI 2025 observations suggesting dynamic dark energy. The baryon asymmetry parameter η is estimated as: η = α³/16π² ≈ 6.1 × 10⁻¹⁰ within 1.7% of the observed value, where the factor 16 = 2⁴ is identified with the Dirac spinor structure of 4-dimensional spacetime. Separation of the four fundamental forces through the running coupling constant α is outlined. This work explores the Planck Sphere as a candidate for the minimal geometric unit of the root field Ψ₀ in Origin Field Theory (OFT), and attempts to present a verifiable framework pointing toward a unified description of both OFT and Virtual Gravity Theory (VGT).

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-16
DOI
https://doi.org/10.5281/zenodo.20736648
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

Planck Sphere Cosmology: The Minimal Unit of the Universe and Its Unified Description of Fundamental Physics

Tsutomu Ishii
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

Planck Sphere Cosmology: The Minimal Unit of the Universe and Its Unified Description of Fundamental Physics

Tsutomu Ishii
preprint en

Abstract

This paper proposes the Planck Sphere — a sphere of radius equal to the Planck length ℓP — as the minimal geometric unit of the universe. Starting from the core identity: A_P × c³ = 4π × ℏ × G we demonstrate that the fundamental constants of nature (c, G, ℏ) are mutually determined through the Planck Sphere's surface area AP and the geometric factor 4π. From this single relation, we derive the Planck length, time, energy, mass, and temperature, as well as the information content of the Planck Sphere (I = π bits). Extended equivalences incorporating electromagnetic (ε₀, qP) and thermal (kB, TP) quantities are shown to follow naturally. We further propose that the cosmological constant Λ is not a true constant but varies as Λ(t) ~ 1/R(t)², consistent with recent DESI 2025 observations suggesting dynamic dark energy. The baryon asymmetry parameter η is estimated as: η = α³/16π² ≈ 6.1 × 10⁻¹⁰ within 1.7% of the observed value, where the factor 16 = 2⁴ is identified with the Dirac spinor structure of 4-dimensional spacetime. Separation of the four fundamental forces through the running coupling constant α is outlined. This work explores the Planck Sphere as a candidate for the minimal geometric unit of the root field Ψ₀ in Origin Field Theory (OFT), and attempts to present a verifiable framework pointing toward a unified description of both OFT and Virtual Gravity Theory (VGT).

Zenodo (CERN European Organization for Nuclear Research)
Nagano University (JP)
Cosmology and Gravitation Theories
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